Postavljanje jednacina
clear variables
syms ug uC uL L C DiL DuC m u iC iL Um t
jednacine = [ug == uC + uL,...
uL == L*DiL,...
iC == C*DuC,...
uL==m*u,...
iC==iL]
jednacine = 
Eliminacija i redukcija sistema
sistem = eliminate(jednacine, [uL,iC,u])
sistem = 
Resavanje po izvodima stanja
resenje = solve(sistem, [DiL,DuC])
resenje = struct with fields:
DiL: -(uC - ug)/L DuC: iL/C
Resavanje sistema diferencijalnih jednacina
syms iL(t) uC(t)
jednacineStanjaFun = subs([diff(uC)==resenje.DuC; diff(iL)==resenje.DiL], {iL,uC}, {iL(t),uC(t)})
jednacineStanjaFun(t) = 
zamene = ug==Um*sin(t/sqrt(C*L))*heaviside(t)
zamene = 
jednacineStanjaFunR=subs(jednacineStanjaFun,lhs(zamene),rhs(zamene))
jednacineStanjaFunR(t) = 
assume(t>0 & C>0 & L>0)
resenjeDiff=dsolve(jednacineStanjaFunR,[uC(0)==0,iL(0)==0],'IgnoreAnalyticConstraints',false)
resenjeDiff = struct with fields:
iL: cos(t/(C^(1/2)*L^(1/2)))*((C^(1/2)*Um)/(2*L^(1/2)) - (C^(1/2)*Um*cos(t/(C^(1/2)*L^(1/2)))^2)/(2*L^(1/2))) + sin(t/(C^(1/2)*L^(1/2)))*((Um*t)/(2*L) - (C^(1/2)*Um*sin((2*t)/(C^(1/2)*L^(1/2))))/(4*L^(1/2))) uC: (L^(1/2)*sin(t/(C^(1/2)*L^(1/2)))*((C^(1/2)*Um)/(2*L^(1/2)) - (C^(1/2)*Um*cos(t/(C^(1/2)*L^(1/2)))^2)/(2*L^(1/2))))/C^(1/2) - (L^(1/2)*cos(t/(C^(1/2)*L^(1/2)))*((Um*t)/(2*L) - (C^(1/2)*Um*sin((2*t)/(C^(1/2)*L^(1/2))))/(4*L^(1/2))))/C^(1/2)
simplify(resenjeDiff.iL)
ans = 
numzamene=[L==1e-4, C==1e-6, Um==1, m==1]
numzamene = 
fplot(t, subs(resenjeDiff.iL, lhs(numzamene), rhs(numzamene)),[0 0.002])